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Effects of key parameters on the seismic design of reinforced concrete framed joints.

Introduction

Earthquakes are one of the most feared natural phenomena that are relatively unexpected and whose impact is sudden due to the almost instantaneous destruction that a major earthquake can produce. Beam column joints can be critical regions in reinforced concrete frames designed for inelastic response to severe seismic attack. As a consequence of seismic moments in columns of opposite signs immediately above and below the joint, the joint region is subjected to horizontal and vertical shear forces whose magnitude is typically many times higher than in the adjacent beams and columns. If not designed for, joint shear failure can take place. [1, 2] The reversal in moment across the joint also means that the beam reinforcement is required to be in compression on one side of the joint and at tensile yield on the other side of the joint. The high bond stress required to sustain this force gradient across the joint may cause bond failure and corresponding degradation of moment capacity accompanied by excessive drift.

In the analysis of reinforced concrete moment resisting frames the joints are generally assumed as rigid. In Indian practice, the joint is usually neglected for specific design with attention being restricted to provision of sufficient anchorage for beam longitudinal reinforcement. This may be acceptable when the frame is not subjected to earthquake loads. There have been many catastrophic failures reported in the past earthquakes, in particular with Turkey and Taiwan earthquakes occurred in 1999, which have been attributed to beam-column joints. The poor design practice of beam column joints is compounded by the high demand imposed by the adjoining flexural members (beams and columns) in the event of mobilizing their inelastic capacities to dissipate seismic energy. Unsafe design and detailing within the joint region jeopardizes the entire structure, even if other structural members conform to the design requirements. [2, 3]

Since past three decades extensive research has been carried out on studying the behaviour of joints under seismic conditions through experimental and analytical studies. Various international codes of practices have been undergoing periodic revisions to incorporate the research findings into practice. The paper is aimed at making designers aware of the theoretical background on the design of beam column joints highlighting important parameters affecting seismic behaviour of joints.

Shear strength

Internal forces transmitted from adjacent members to the joint as shown in fig1. result in joint shear forces in both the horizontal and vertical directions. These shear forces lead to diagonal compression and tension stresses in the joint core. The latter will usually result in diagonal cracking of the concrete core. The mechanism of shear resistance at this stage changes drastically. [6]

[FIGURE 1 OMITTED]

Some of the internal forces, particularly those generated in the concrete, will combine to develop a diagonal strut. Other forces, transmitted to the joint core form beam and column by means of bond, necessitate a truss mechanism.

To prevent shear failure by diagonal tension, usually along a potential corner to corner failure plane. Both the horizontal and vertical shear reinforcement will be required. Such reinforcement will enable a diagonal compression field to be mobilized, which provides a feasible load path for both horizontal and vertical shear forces .The amount of horizontal joint shear reinforcement required, may be significantly more than would normally be provided in columns in the form of ties or hoops, particularly when axial compression on columns is small.

When the joint shear reinforcement is sufficient, yielding of the hoops will occur. Irrespective of the direction of diagonal cracking, horizontal shear reinforcement transmits tension forces only. The inelastic steel strains that may result are irreversible. Consequently, during subsequent loading, stirrup ties can make a significant contribution to shear resistance only if the tensile strains imposed are larger then those developed previously. This then leads to drastic loss of stiffness art low shear force levels, particularly immediately after a force or displacement reversal. [5]

Bond strength

At exterior column the difficulty in anchoring a beam bear of full strength can be overcome readily by providing a standard hook. At interior columns, however, this is impractical. Some codes require that beam bars at interior beam-column joints must pass continuously that bars may be anchored with equal if not greater efficiency using standard hooks within or immediately behind an interior joint.

The fact that bars passing through interior joints are being "pulled" as well "pushed" by the adjacent beams, to transmit forces corresponding to steel stresses up to the strain hardening range in tension, has not as a rule, been take into account code specifications until recently. In most practical situations bond stresses required to transmit bar forces to the concrete of the joint core consistent with plastic hinge development at both sides of the joint, would be very large and well beyond limits considered by codes for bar strength development. [7] Even at moderate ductility demands, a slip of beam bars through the joint can occur. A breakdown of bond within interior joints does not necessarily result in sudden loss of strength. [8]

Present Work

A Ground plus four storey building in zone V has been analysed with the aid of computer software. In zone-V the building is designed in three cases by varying the column B/D ratios and concrete compressive strength and the amount of joint shear in three different locations viz. interior, exterior, and corner are compared. This building form a representative group of medium rise buildings which of lately have been included to be designed as only SMRF. This building does not have any shear walls. Seismic forces in each building have been obtained using equivalent static method. Ductility provisions of IS: 13920-1993 and IS: 13920 (Draft) will mainly influence design of columns, beams and joints. Hence the quantity of reinforcement in slabs, foundations and other structural and non-structural elements has not been considered. The beam and column size has not been varied for the two design approaches.

Modelling of Building Frame

A G+4 storey building having panel aspect ratio 1.25 for first two bays and 1.67 for middle bay is analysed and designed for seismic forces in Zone V as SMRF respectively using ETABS version-8.4.8.. The plan and sectional elevation of the building is shown in the figures 2, 3 and 4. The schedule of member sizes of the frame for three cases is as shown in Table 1, 2 and 3.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]
Genera data:

Grade of concrete                         : M20, M25, M30
Grade of steel considered                 : Fe 250, Fe 415
Live load on roof                         : 1.5 KN/[m.sup.2] (Nil for
                                            earthquake)
Live load on floors                       : 3.0 KN/[m.sup.2] (25 % for
                                            earthquake)
Roof finish                               : 1.0 KN/[m.sup.2]
Floor finish                              : 1.0 KN/[m.sup.2]
Brick wall on peripheral beams            : 230 mm thick
Brick wall on Internal beams              : 150 mm thick
Density of concrete                       : 25 KN/[m.sup.3]
Density of brick wall Including plaster   : 20 KN/[m.sup.3]


Design of beams and columns has been done by limit state method taking analysis results from ETABS version--8.4.8. Shear reinforcement in beams is obtained for design shear force at supports and at centre. For detailing main reinforcement in beams, the available diameters of steel ranging from 12 to 20 mm has been used and a set of arrangement is provided that is closest to theoretical area of steel required. If two members are on either side of a column and are continuous in alignment, the same reinforcement is provided on both sides of the column by picking up the higher steel area. The minimum and maximum reinforcement requirements are also checked.

In addition to detailing of beams as in above, in the design of beams in SMRF it is also ensured that the positive steel at support is at least half the negative steel provided at that support or joint. The steel provided at each of the top and bottom face of the member at any section along its length is more than one fourth of the maximum negative moment steel provided at the face of either joint. All other requirements are checked as per clauses given in IS: 13920-1993.

In the design of columns, for design axial forces and biaxial moments generated using ETABS version--8.4.8 and steel area obtained, a steel arrangement corresponding to the required steel area is provided equally distributed on all four sides of sections. In addition to design and detailing of main reinforcement in columns, confinement steel as required by IS: 13920-1993 (12,13) is calculated and provided the same over the required length at ends of column in SMRF. This enabled a fairly comprehensive and reliable estimation of reinforcement quantities. The design results are provided in tabular format. The ductile design of interior joint is shown for illustration.

Interior Joint Design

The details of the column and beam reinforcement meeting at the joint are shown in Figure 5.

[FIGURE 5 OMITTED]

The transverse beam of size 300 x 600 is reinforced with 6-20 [empty set] + 3-16 [empty set] (2489.13 [mm.sup.2], i.e., 1.5596%) at top and 3-20 [empty set] + 4-16 [empty set] (1747.429 [mm.sup.2], i.e., 1.0948%) at bottom. The hogging and sagging moment capacity is evaluated as 391.422 KN-m and 321.638 KN-m, respectively. The longitudinal beam of size 300 x 600 mm is reinforced with 4-20 [empty set] + 2-16 [empty set] + 5-12 [empty set] (2225 [mm.sup.2], i.e. 1.394%) at top and 3-20 [empty set] + 3-16 [empty set] + 1-12 [empty set] (1659.429 [mm.sup.2] i.e. 1.0397%) at bottom. The hogging and sagging moment capacity is evaluated as 348.119 KN-m and 305.138 KN-m, respectively.

Check for Earthquake in X-Direction Column Shear

The column shear is as explained below for sway to right and left conditions respectively.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

For both the above case the column shear is

[V.sub. col] = 1.4 [[M.sub.s] + [M.sub.h]] / [h.sub.st]

[V.sub. col] = 1.4 [348.12 + 305.14] / 3

[V.sub. col] = 304.854 KN

Force Developed in Beam Reinforcement

Figures 8 (a) and 8 (b) shows the development of forces in the joint due to beam reinforcement, for sway to right and left, respectively.

[FIGURE 8 OMITTED]

Force developed in the top bars

[T.sub.1] = [A.sub.st] x 1.25 x [f.sub.y] = 2225.143 x 1.25 x 415 /1,000 = 1154.292 KN = [C.sub.1]

The factor 1.25 is to account for the actual ultimate strength being higher than the actual yield strength. [Draft revision of IS 13920]

Force developed in the bottom bars = [T.sub.2]

= Ast x 1.25 x fy = 1659.429 x 1.25 x 415 /1,000

= 860.828 KN = [C.sub.2]

Joint Shear

The forces acting on the joint region are shown in the fig. 9 By considering Equilibrium of forces acting on the joint, it is found that the joint shear as

[V.sub.Joint] = T + C - [V.sub.col] Where T is Tension I beam bars C is Compression in beam bars [V.sub.col] is column shear

[FIGURE 9 OMITTED]

[V.sub.Joint] = [T.sub.1] + [C.sub.2] - [V.sub.col]

= 1154.292 + 860.828 -304.854

= 1710.268 KN

Maximum value of [T.sub.1] and minimum value of [V.sub.col] is used in the above equation.

Check for Joint Shear Strength

The effective width provisions for joints are shown in Figure 10 The calculation of the effective width of the joint and the design shear strength of the joint is based on the draft revision of IS 13920:1993. (14)

[FIGURE 10 OMITTED]

The effective width of the joint is lesser of the

i) [b.sub.j] = [b.sub.b] + 0.5 x [h.sub.c]

ii) [b.sub.j] = [b.sub.c]

Effective width for joint

i) [b.sub.j] = [b.sub.b] + [h.sub.c]/2

= 300 + 400 /2 = 500 mm

or

ii) [b.sub.j] = [b.sub.c] = 400 mm

Take effective width as 400 mm.

[h.sub.c] = full depth of column = 500 mm

Effective shear area of the joint

= Aej = [b.sub.j] [h.sub.c] = 400 x 500 = 20000 [mm.sup.2]

Shear strength of joint confined on two opposite faces, as per Clause 8.1.3 of draft revision of IS13920 shear strength of the joint in X-direction is

= 1.0 [square root (f[sub.ck][A.sub.ej])] = (1.0 x 20 x 400 x 500) /1,000 = 894.427 KN < 1,624 KN

Hence, not Safe.

Check for Flexural Strength Ratio

The hogging and sagging moment capacities of the longitudinal beam in X-direction are as 348.119 KN-m and 305.138 KN-m. The column is reinforced with 8 - 32 [empty set] + 6 - 20 [empty set] bars with total Asc = 8322.285 [mm.sup.2] i.e. 8322.285 x 100 / (400 x 500) = 4.161%. p/fck = 4.161 / 20 = 0.208. It is conservative here to calculate the moment capacity of column with zero axial loads. In actual practice it is desirable to take minimum [M.sub.u] / f [sub.ck]b [D.sup.2] corresponding to actual [P.sub.u] / f [sub.ck]b [D.sup.2] obtained from different load combinations. Referring to chart 44, of SP:34,15 corresponding to [P.sub.u] / f [sub.ck]b [D.sup.2] = 0.00 at

[A.sub.B], for p/[f.sub.ck] = 0.208 and d'/D = (40 + 25 /2) / 400 = 0.13125, we get [M.sub.u] / f [sub.ck]b [D.sup.2] = 0.225

[M.sub.u] = (0.225 x 20 x 500 x 400 x 400) / 1x[10.sup.6] = 360 KN-m

Referring to Figure 5.10, the joint is checked for strong column - weak beam condition.

[FIGURE 11 OMITTED]

[SIGMA][M.sub.c] = 360+360 = 720 KN-m [SIGMA][M.sub.b] = 348.119 + 305.138 = 653.258 KN-m [SIGMA][M.sub.c]/[SIGMA][M.sub.b] = 720 /653.258 = 1.102 > 1.1

Hence, requirement of strong column-weak beam condition as per proposed draft IS 13920 is satisfied as per Clause 7.2.1 of IS 13920 proposed draft.

Check for Earthquake in Y-Direction Column Shear

The column shear is as explained below for sway to right and left conditions respectively.

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

For both the above case the column shear is

[V.sub.col] = 1.4 [[M.sub.s] + [M.sub.h]] / [h.sub.st]

[V.sub.col] = 1.4 [391.422 + 321.638] / 3

[V.sub.col] = 332.761KN

Force Developed in Beam Reinforcement

Figures 14(a) and 14(b) show the development of forces in the joint due to beam reinforcement, for sway to right and left, respectively.

[FIGURE 14 OMITTED]

Force developed in the top bars

T1 = Ast x 1.25 x fy = (2489.13 x 1.25 x 415) /1,000 = 1291.236 KN = [C.sub.1]

The factor 1.25 is to account for the actual ultimate strength being higher than the actual yield strength. [Draft revision of IS 13920]

Force developed in the bottom bars

[T.sub.2] = Ast x 1.25 x fy = (1747.429 x 1.25 x 415) /1,000 = 906.478 KN = [C.sub.2]

Joint Shear

The forces acting on the joint region are shown in the fig.15 By considering Equilibrium of forces acting on the joint, we get the joint shear as

[FIGURE 15 OMITTED]

[V.sub.Joint] = [T.sub.1] + [C.sub.2] - [V.sub.col] = 1291.236 + 906.478 -332.761= 1864.953 KN Maximum value of T1and minimum value of Vcol is used in the above equation.

Check for Joint Shear Strength

The effective width provisions for joints are shown in figure16. The calculation of the effective width of the joint and the design shear strength of the joint is based on the draft revision of IS 13920:1993.

[FIGURE 16 OMITTED]

The effective width of the joint is lesser of the

i) [b.sub.j] = [b.sub.b] + 0.5 x [h.sub.c]

ii) [b.sub.j] = [b.sub.c]

Effective width for joint

i) [b.sub.j] = [b.sub.b] + [h.sub.c]/2 = 300 + 500 /2 = 550 mm

or

ii) [b.sub.j] = [b.sub.c] = 400 mm

Take effective width as 400 mm.

[h.sub.c] = full depth of column = 500 mm

Effective shear area of the joint

= [A.sub.ej] = [b.sub.j] [h.sub.c] = 400 x 500 = 20000 [mm.sup.2]

Shear strength of joint confined on two opposite faces, as per Clause 8.1.3 of draft revision of IS13920 shear strength of the joint in X-direction is = 1.2 [square root (f [sub.ck] [A.sub.ej])] = (1.2 x 20 x 400 x 500) /1,000 = 1073.313 KN < 1,624 KN

Hence, not Safe.

Check for Flexural Strength Ratio

The hogging and sagging moment capacities of the transverse beam are as 391.422 KN-m and 321.638 KN-m, respectively. The column is reinforced with 8 - 32[empty set] + 6 - 20 [empty set] bars with total Asc = 8322.285 [mm.sup.2] i.e. 8322.285 x 100 / (400 x 500) = 4.161%. p/[f.sub.ck] = 4.161 / 20 = 0.208. It is conservative here to calculate the moment capacity of column with zero axial loads. In actual practice it is desirable to take minimum [M.sub.u] / f [sub.ck]b [D.sup.2] corresponding to actual [P.sub.u] / f [sub.ck]b D obtained from different load combinations. Referring to chart 44, of SP: 16, corresponding to [P.sub.u] / f [sub.ck]b D = 0.00 at [A.sub.B], for p/[f.sub.ck] = 0.208 and d'/D = (40 + 25 /2) / 500 = 0.105, we get [M.sub.u] / f [sub.ck]b [D.sup.2] = 0.245 Mu = 0.245 x 20 x 400 x 500 x 500 / 1x[10.sup.6] = 490 KN-m

Referring to figure 17 the joint is checked for strong column - weak beam

[FIGURE 17 OMITTED]

[SIGMA] [M.sub.c] = 490+490 = 980 KN-m [SIGMA] [M.sub.b] = 377 + 246 = 623 KN-m = 760 /623 = 1.374 > 1.1

Hence, requirement of strong column-weak beam condition as per proposed draft IS 13920 is satisfied as per Clause 7.2.1 of IS 13920 proposed draft.

Confining Reinforcement

Special confining reinforcement is provided over a length of lo from each joint where [l.sub.0] is maximum of larger lateral dimension of member = 400 mm clear span/ 6 = 2400/ 6 = 400 mm 450 mm

So provide special confining reinforcement for length 450mm on either side of the joint.

Spacing of confining hoop shall not exceed 1/ 4 minimum dimension of the column member = 400/ 4 = 100 mm 100 mm The spacing need not be less than 75 mm Taking 10 mm diameter bar for confining hoop

[A.sub.sh] = 0.18XSXShX [f.sub.ck]/[f.sub.y] x [([A.sub.g/[A.sub.k]])-1]

78.54 = 0.18 X S X 188.5 X 20/415 X [400 X 500 / 336 X 436] -1

S =131.44 mm

Hence provide 10# @ 100 mm c/c as confining links.

Results and Discussion

As can be seen from the checks in section and the joint is not safe. Joint region requires higher grades of concrete. Higher grades of concrete is undesirable, in such cases the following three alternatives can be tried.

i) Increase the column section so that the joint area is increased. This will also reduce the main longitudinal steel requirement in the column owing to larger column size.

ii) Increase the size of the beam section. If this option is adopted, it is advisable to increase the depth of the beam. This will reduce the steel required in the beam and hence will reduce the joint shear. In case of depth restriction in the beam, increase in beam width can be considered if the difference between the shear strength of joint and joint shear is small.

iii) Increase the grade of concrete. This option will increase the shear strength of joint and also reduce the steel required in columns.

From the above three options, column dimensions and concrete compressive strength are considered for the re-analysis. The reanalysis and design is performed for three sets of column dimensions for different concrete compressive strengths. The results obtained in the three cases are shown in the following tables and figures.

Conclusions

* For non-seismic loads column shear alone is acting as the joint shear, whereas in seismic conditions contribution of beam forces developed by seismic loads is also considered in the joint shear calculation.

* For medium rise buildings in Zone-V, joint shear is 18 to 20 times more for seismic loads than in non-seismic loads.

* The joint shear strength can be increased with increase in concrete compressive strength, and column B/D ratio. However, there is no increase in joint shear strength observed, while changing the beam B/D ratio.

* In seismic zones V, minimum grade of concrete is M30. M25, which can be used for beams and columns with rich mix concrete in joint regions.

* In all cases roof joint are safe against joint shear but the column reinforcement should be provided in the roof column to satisfy the strong column weak beam condition.

* In an exterior joint and a corner joint the depth of the column should be provided to satisfy the anchorage requirements of the beam longitudinal bar.

* Joint shear in floor joints is 3 to 5 times more than the roof joints.

[FIGURE 18 OMITTED]

[FIGURE 19 OMITTED]

[FIGURE 20 OMITTED]

[FIGURE 21 OMITTED]

[FIGURE 22 OMITTED]

[FIGURE 23 OMITTED]

[FIGURE 24 OMITTED]

[FIGURE 25 OMITTED]

[FIGURE 26 OMITTED]

[FIGURE 27 OMITTED]

References

[1] Paulay, T. and Priestley, M. J. N. (1992), Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley and Sons.

[2] Subramanian, N. and Prakash Rao, D. S., 2003, "Seismic Design of Joints in RC Structures," The Indian Concrete Journal, 77(2), pp 883-892.

[3] Ichinose, T., 1991, "Interaction between bond at beam bars and shear reinforcement in RC interior joints", Design of Beam-Column Joints for Seismic Resistance, SP-123, American Concrete Institute, Farmington Hills, Mich., pp 379-400.

[4] French, C.W. and Moehle, J. P., 1991, "Effect of floor slab on behavior of slab-beam-column connections," Design of Beam-Column Joints for Seismic Resistance, SP-123, American Concrete Institute, Farmington Hills, Mich., pp 225-258.

[5] Leon, R.T., 1990, "Shear Strength and Hysteretic Behavior of Beam-Column Joints," ACI Structural Journal, 87(1), pp 3-11.

[6] Uma, S. R., "Seismic Behaviour of Beam Column Joints in Moment Resisting Reinforced Concrete Frame Structures," submitted to Indian Concrete Journal, October 2004

[7] Wakabayashi, M., Minami, K., Nishimura, Y. and Imanaka, N., 1983, "Anchorage of bent bar in reinforced concrete exterior joints," Transactions of the Japan Concrete Institute, 5, pp 317-324.

[8] Paulay, T., Park, R. and Priestley, M. J. N. (1978), "Reinforced Concrete Beam-Column Joints under Seismic Actions," Journal of ACI, 75(11), 585-593

[9] Park, R. and Hopkins, D. C., 1989, "United States/New Zealand/Japan/China Collaborative Research Project on the Seismic Design of Reinforced Concrete Beam-Column-Slab Joints," Bulletin of the New Zealand National Society for Earthquake Engineering, 22(2), pp 122-126.

[10] ACI 352R-02, 2002, "Recommendations for design of beam-column-joints in monolithic reinforced concrete structures," American Concrete Institute, ACIASCE, Committee 352, Detroit

[11] ENV 1998-1:2003, "General Rules-Specific Rules for Various Materials and Elements," Eurocode 8:

[12] IS: 456-2000, "Indian Standard code of practice for plain and reinforced concrete," Bureau of Indian Standards, New Delhi.

[13] IS: 13920-1993, "Indian Standard code of practice for ductile detailing of concrete structures subjected

[14] IS: 13920-Draft, "Indian Standard code of practice for ductile detailing of concrete structures subjected to seismic forces, Bureau of Indian Standards, New Delhi, 1993.

[15] SP: 34 (S&T)- 1987, "Handbook on concrete reinforcement detailing,", Bureau of Indian Standards, New Delhi.

Yogesh D. Patil (1), H.S. Patil (2) and M.N.K.A. Raju (3)

(1) Lecturer, Applied Mechanics Dept., E-mail: chipatil@yahoo.com

(2) Professor, Applied Mechanics Dept., E-mail: hsp57@yahoo.com

(3) P.G. Student, Structural Engg., E-mail: mullapudi_raju@inbox.com S.V. National Institute of Technology, Surat -395007, India
Table 1: Schedule of member sizes (Case-1)

  COLUMNS                     BEAMS

C1   300 X 500          RB1,FB1   300 X 600
C2   400 X 400          RB2,FB2   300 X 600
C3   400 X 500          PB1       300 X 400
Slab thickness 125 mm   PB2       300 X 350

Note : All dimensions are in mm

Table 2: Schedule of member sizes (Case-2)

 COLUMNS                       BEAMS

C1   500 X 500          RB1,FB1   300 X 600
C2   500 X 500          RB2,FB2   300 X 600
C3   500 X 600          PB1       300 X 400
Slab thickness 125 mm   PB2       300 X 350

Note : All dimensions are in mm

Table 3: Schedule of member sizes (Case-3)

  COLUMNS                    BEAMS
C1   500 X 500          RB1,FB1   300 X 600
C2   400 X 500          RB2,FB2   300 X 600
C3   600 X 600          PB1       300 X 400

Slab thickness 125 mm   PB2       300 X 350

Note : All dimensions are in mm

Table 4: Joint shear details at Roof level for case-1 (Zone-V)

fy      415            N/[mm.sup.2]   Dimensio       B (mm)
                                      Beam X-Dir     300
Zone    V                             Beam Y-Dir     300
                              CASE-1

Joint   Concrete       Location       Direction      Joint
        compressiv                                   shear
        e strength                                   strength
        N/[mm.sup.2]                                 KN

INTERIOR

1       20              Roof          Y--Direction   1073.31
                                      X--Direction    894.43
2       25              Roof          Y--Direction   1200
                                      X--Direction   1000
3       30              Roof          Y--Direction   1314.534
                                      X--Direction   1095.445

EXTERIOR

4       20              Roof          Y--Direction    670.82
                                      X--Direction    603.74
5       25              Roof          Y--Direction    750
                                      X--Direction    675
6       30              Roof          Y--Direction    821.583
                                      X--Direction    739.425

CORNER

7       20              Roof          Y--Direction    715.54
                                      X--Direction    715.54
8       25              Roof          Y--Direction    800
                                      X--Direction    800
9       30              Roof          Y--Direction    876.35
                                      X--Direction    876.35

fy      D (mm)        Columns    B (mm)          D (mm)
        600           Interior   400             500
Zone    600           Exterior   300             500
                      Corner     400             400

        CASE-1

Joint   Joint shear   Result     Strong          Confining links
        calculated               column
        KN                       Weak beam
                                 condition

INTERIOR

1       492.7         Safe       Satisfied       10# 100 mm C/C
        440.95        Safe       Satisfied       10# 100 mm C/C
2       465.31        Safe       Satisfied       10# 80 mm C/C
        423.74        Safe       Satisfied       10# 80 mm C/C
3       503.325       Safe       Satisfied       10# 75 mm C/C
        462.45        Safe       Satisfied       10# 75 mm C/C

EXTERIOR

4       283.65        Safe       Satisfied       10# 80 mm C/C
        468.935       Safe       Not Satisfied   10# 80 mm C/C
5       280.8         Safe       Satisfied       10# 75 mm C/C
        467.72        Safe       Not Satisfied   10# 75 mm C/C
6       222.11        Safe       Satisfied       10# 75 mm C/C
        467.72        Safe       Not Satisfied   10# 75 mm C/C

CORNER

7       198.376       Safe       Satisfied       10# 100 mm C/C
        185.76        Safe       Satisfied       10# 100 mm C/C
8       202.333       Safe       Satisfied       10# 85 mm C/C
        185.211       Safe       Satisfied       10# 85 mm C/C
9       234.112       Safe       Satisfied       10# 75 mm C/C
        230.154       Safe       Satisfied       10# 75 mm C/C

Table 5: Joint shear details at Second floor level for case-1 (Zone-V)

fy      415            N/[mm.sup.2]   Dimension      B (mm)
                                      Beam X-D       300
ZONE    V                             Beam Y-D       300

                             CASE-1

Joint   Concrete       Location       Direction      Joint
        comp.                                        shear
        strength                                     strength
        N/[mm.sup.2]                                 KN

INTERIOR

1       20             Floor          Y--Direction   2078.46
                                      X--Direction   1732.05
2       25             Floor          Y--Direction   2078.46
                                      x--Direction   1732.05
3       30             Floor          Y--Direction   2007.98
                                      X--Direction   1673.32

EXTERIOR

4       20             Floor          Y--Direction   1209.339
                                      X--Direction   1088.405
5       25             Floor          Y--Direction   1209.339
                                      X--Direction   1088.405
6       30             Floor          Y--Direction   1209.339
                                      X--Direction   1073.313

CORNER

7       20             Floor          Y--Direction   1011.928
                                      X--Direction   1011.928
8       25             Floor          Y--Direction   1011.928
                                      X--Direction   1011.928
9       30             Floor          Y--Direction   1073.313
                                      X--Direction   1073.313

fy      D (mm)       Columns    B (mm)          D (mm)
        600          Interior   400             500
ZONE    600          Exterior   300             500

        CASE-1       Corner     400             400

Joint   Joint        Result     Strong          Confining links
        shear                   column
        calculated              Weak beam
        KN                      condition

INTERIOR

1       1864.95      Not Safe   Satisfied       10# 75 mm C/C
        1710.26      Not Safe   Satisfied       10# 75 mm C/C
2       1860.87      Not Safe   Satisfied       10# 75 mm C/C
        1688.54      Not Safe   Satisfied       10# 75 mm C/C
3       1891.163     Not Safe   Satisfied       10# 75 mm C/C
        1664.71      Not Safe   Satisfied       10# 75 mm C/C

EXTERIOR

4       1197.46      Not Safe   Satisfied       10# 75 mm C/C
        1058.61      Not Safe   Not Satisfied   10# 75 mm C/C
5       1199.21      Not Safe   Satisfied       10# 75 mm C/C
        1012.079     Not Safe   Not satisfied   10# 75 mm C/C
6       1201.433     Not Safe   Satisfied       10# 75 mm C/C
        1010.339     Not Safe   Not satisfied   10# 75 mm C/C

CORNER

7       982.56       Not Safe   Satisfied       10# 100 mm C/C
        967.735      Not Safe   Not satisfied   10# 100 mm C/C
8       982.756      Not Safe   Satisfied       10# 85 mm C/C
        970.984      Not Safe   Not satisfied   10# 85 mm C/C
9       930.009      Not Safe   Satisfied       10# 75 mm C/C
        1023.65      Not Safe   Not satisfied   10# 75 mm C/C

Table 6: Joint shear due to Non-seismic and seismic forces
(Interior joint)

Concrete       Joint Shear   Nominal       Joint Shear   Joint Shear
comp.          in (Y-Dir)    Joint shear   in (Y-Dir)    in (X-Dir)
strength       Non-Seismic   strength      Seismic       Non-Seismic
N/[mm.sup.2]   (KN)          (KN)          (KN)          (KN)

15             23.528         929.51       1867.14       77.182
20             73.01         1073.31       1864.95       84.78
25             93.175        1200          1860.87       93.175
30             93.175        1314.534      1891.163      93.175

Concrete       Nominal       Joint Shear
comp.          Joint shear   in (X-Dir)
strength       strength      Seismic
N/[mm.sup.2]   (KN)          (KN)

15             774.596       1652.46
20             894.427       1710.26
25             1000          1688.54
30             1095.445      1664.71

Table 7: Joint shear details at Second floor level for case-2 (Zone-V)

fy      415            N/[mm.sup.2]   Dimensions     B (mm)
                                      BEAM X-DIR     300
ZONE    V                             BEAM Y-DIR     300

                       CASE-2

Joint   fck            Location       Direction      Joint shear
        N/[mm.sup.2]                                 strength
                                                     KN

INTERIOR

1       20             FLOOR          Y--DIRECTION  1774.823
                                      X--DIRECTION  1626.922
2       25             FLOOR          Y--DIRECTION  1774.823
                                      X--DIRECTION  1626.922
3       30             FLOOR          Y--DIRECTION  1774.823
                                      X--DIRECTION  1626.922

EXTERIOR

4       20             FLOOR          Y--DIRECTION  1369.306
                                      X--DIRECTION  1369.306
5       25             FLOOR          Y--DIRECTION  1250
                                      X--DIRECTION  1250
6       30             FLOOR          Y--DIRECTION  1369.306
                                      X--DIRECTION  1369.306

CORNER

7       20             FLOOR          Y--DIRECTION  1118.034
                                      X--DIRECTION  1118.034
8       25             FLOOR          Y--DIRECTION  1250
                                      X--DIRECTION  1250
9       30             FLOOR          Y--DIRECTION  1369.306
                                      X--DIRECTION  1369.306

fy      D (mm)        Columns    B (mm)      D (mm)
        600           Interior   500         600
ZONE    600           Exterior   500         500

                      Corner     500         500

Joint   joint shear   Result     Strong      Confining links
        calculated               column
        KN                       Weak beam
                                 condition

INTERIOR

1       1736.229      SAFE       SATISFIED   10# 75 mm C/C
        1256.04       SAFE       SATISFIED   10# 75 mm C/C
2       1689.6        SAFE       SATISFIED   10# 75 mm C/C
        1310.161      SAFE       SATISFIED   10# 75 mm C/C
3       1680.084      SAFE       SATISFIED   10# 75 mm C/C
        1216.074      SAFE       SATISFIED   10# 75 mm C/C

EXTERIOR

4       1056.62       SAFE       SATISFIED   10# 100 mm C/C
        1259.977      SAFE       SATISFIED   10# 100 mm C/C
5       1060.188      SAFE       SATISFIED   10# 90 mm C/C
        1142.925      SAFE       SATISFIED   10# 90 mm C/C
6       1062.17       SAFE       SATISFIED   10# 75 mm C/C
        1136.299      SAFE       SATISFIED   10# 75 mm C/C

CORNER

7        972.853      SAFE       SATISFIED   10# 100 mm C/C
         841.514      SAFE       SATISFIED   10# 100 mm C/C
8       1010.477      SAFE       SATISFIED   10# 90 mm C/C
         830.451      SAFE       SATISFIED   10# 90 mm C/C
9       1011.402      SAFE       SATISFIED   10# 75 mm C/C
         771.757      SAFE       SATISFIED   10# 75 mm C/C

Table 8: Joint shear details at Second floor level for case-3 (Zone-V)

fy      415            N/[mm.sup.2]   BEAMS          B (mm)

                                      X--Direction   300
Zone    V                             Y--Direction   300

                                      CASE-3

Joint   fck            Location       Direction      Joint shear
        N/[mm.sup.2]                                 strength
                                                     KN

INTERIOR

1       20             Floor          Y--Direction   1971.8
                                      X--Direction   1971.8
2       25             Floor          Y--Direction   1800
                                      X--Direction   1800
3       30             Floor          Y--Direction   1774.823
                                      X--Direction   1774.823

EXTERIOR

4       20             Floor          Y--Direction   1095.445
                                      X--Direction   1095.445
5       25             Floor          Y--Direction   1095.445
                                      X--Direction   1095.445
6       30             Floor          Y--Direction   1095.445
                                      X--Direction   1095.445

CORNER

7       20             Floor          Y--Direction   1118.034
                                      X--Direction   1118.034
8       25             Floor          Y--Direction   1250
                                      X--Direction   1250
9       30             Floor          Y--Direction   1369.306
                                      X--Direction   1369.306

fy      D (mm)       COLUMN     B (mm)      D (mm)
                     S
        600          Interior   600         600
Zone    600          Exterior   400         500

        CASE-3       Corner     500         500

Joint   Joint        Result     Strong      Confining links
        shear                   column
        calculated              Weak beam
        KN                      condition

INTERIOR

1       1834.707     Safe       Satisfied   10# 80 mm C/C
        1608.131     Safe       Satisfied   10# 80 mm C/C
2       1784.55      Safe       Satisfied   10# 95 mm C/C
        1538.292     Safe       Satisfied   10# 95 mm C/C
3       1759.9       Safe       Satisfied   10# 80 mm C/C
        1515.73      Safe       Satisfied   10# 80 mm C/C

EXTERIOR

4       1040.62      Safe       Satisfied   10# 100 mm C/C
        1052.096     Safe       Satisfied   10# 100 mm C/C
5       1017.55      Safe       Satisfied   10# 80 mm C/C
         969.49      Safe       Satisfied   10# 80 mm C/C
6       1061.37      Safe       Satisfied   10# 75 mm C/C
         983.282     Safe       Satisfied   10# 75 mm C/C

CORNER

7        991.837     Safe       Satisfied   10# 100 mm C/C
         881.22      Safe       Satisfied   10# 100 mm C/C
8       1009.49      Safe       Satisfied   10# 90 mm C/C
         894.263     Safe       Satisfied   10# 90 mm C/C
9        991.837     Safe       Satisfied   10# 75 mm C/C
         823.518     Safe       Satisfied   10# 75 mm C/C
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Article Details
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Author:Patil, Yogesh D.; Patil, H.S.; Raju, M.N.K.A.
Publication:International Journal of Applied Engineering Research
Article Type:Report
Geographic Code:1USA
Date:Nov 1, 2009
Words:5681
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